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arXiv · 1410.1186

Virasoro representations with central charges $\frac{1}{2}$ and 1 on the real neutral fermion Fock space $\mathit{F^{\otimes \frac{1}{2}}}$

Iana I. Anguelova
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Abstract

We study a family of fermionic oscillator representations of the Virasoro algebra via 2-point-local Virasoro fields on the Fock space $\mathit{F^{\otimes \frac{1}{2}}}$ of a neutral (real) fermion. We obtain the decomposition of $\mathit{F^{\otimes \frac{1}{2}}}$ as a direct sum of irreducible highest weight Virasoro modules with central charge $c=1$. As a corollary we obtain the decomposition of the irreducible highest weight Virasoro modules with central charge $c=\frac{1}{2}$ into irreducible highest weight Virasoro modules with central charge $c=1$. As an application we show how positive sum (fermionic) character formulas for the Virasoro modules of charge $c=\frac{1}{2}$ follow from these decompositions.

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BibTeXRIS

Iana I. Anguelova. 2014-10-05. Virasoro representations with central charges $\frac{1}{2}$ and 1 on the real neutral fermion Fock space $\mathit{F^{\otimes \frac{1}{2}}}$. https://doi.org/10.1088/1742-6596%2F563%2F1%2F012001

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